Noncommutative Geometry Seminar

Date: April 4, 2018

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Dima Zanin, UNSW

Title: Connes Character Formula for locally compact spectral triples

Abstract: In this talk, I provide a natural condition on (locally compact) spectral triple which implies a number of interesting corollaries:
1) Asymptotic for heat semigroup. Surprisingly, it was not established before even for compact spectral triples.
2) Existence of the heat semigroup asymptotic easily provides analytic continuation of \zeta-function to a bigger half-plane.
3) Finally, the Connes Character formula in terms of singular traces on the ideal $\mathcal{L}_{1,\infty}.$ This is derived from the analytic continuation of \zeta-function to a neighborhood of the pole.

For compact spectral triples this condition simply defines the class of all smooth p-dimensional spectral triples. This conditions holds in every situation of practical importance: Riemannian manifolds (without assumption of bounded geometry), noncommutative Euclidean spaces etc.